Cruz, a 2016 presidential candidate, has repeatedly warned in recent days that the agreement would mean President Barack Obama's administration is essentially sponsoring terrorism.

"If this deal goes through, the Obama administration will become the leading financier of terrorism against America in the world," Cruz said in a July 15 Fox News interview, for example.

He added: "I've heard this referred to before as the 'Jihadist Stimulus Bill.'"

But Romney argued on Twitter that Cruz's comments undermine the opposition to the deal:

Cruz's campaign did not immediately respond to a request for comment from Business Insider. However, the senator doubled down on his charge against the Obama administration on Tuesday, after the president himself criticized Cruz the day before.

The nuclear deal — struck earlier this month among the US, Iran, and other world powers — grants billions of dollars of sanctions relief in exchange for Tehran curbing its nuclear ambitions. Republican critics like Cruz, who hope to defeat the agreement in Congress, argue that Iran will use the cash windfall to sponsor terror in places like Syria, Lebanon, and Yemen.

"So Mitt Romney's tweet today said, 'Gosh, this rhetoric is not helpful,'" Cruz said. "John Adams famously said, 'Facts are stubborn things.' Describing the actual facts is not using rhetoric; it is called speaking the truth."

Sen. Ted Cruz (R-Texas). Reuters/Gary Cameron

The senator recalled what he described as a critical moment during the 2012 presidential race: a back-and-forth over that year's attack on a diplomatic facility in Benghazi, Libya.

"Part of the reason that Mitt Romney got clobbered by Barack Obama is because we all remember that third debate where Barack Obama turned to Mitt and said, 'I said the Benghazi attack was terrorism and no one is more upset by Benghazi than I am.' And Mitt, I guess listening to his own advice, said, 'Well gosh, I don't want to use any rhetoric. So okay, never mind. I'll just kind of rearrange the pencil on the podium here,'" Cruz said.

He added that the 2016 presidential candidates need to speak up or they will fail like Romney.

"We need to stand up and speak the truth with a smile," he said. "The truth has power and every time we have Republicans who shy away — who don't want to engage, who don't want to speak the truth — we lose."